Nuprl Lemma : correct-sort-arity_wf
∀[opr:Type]. ∀[sort:term(opr) ⟶ ℕ]. ∀[arity:opr ⟶ ((ℕ × ℕ) List)]. ∀[t:term(opr)].
  (correct-sort-arity(sort;arity;t) ∈ ℙ)
Proof
Definitions occuring in Statement : 
correct-sort-arity: correct-sort-arity(sort;arity;t)
, 
term: term(opr)
, 
list: T List
, 
nat: ℕ
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
member: t ∈ T
, 
function: x:A ⟶ B[x]
, 
product: x:A × B[x]
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
correct-sort-arity: correct-sort-arity(sort;arity;t)
, 
let: let, 
implies: P 
⇒ Q
, 
prop: ℙ
, 
and: P ∧ Q
, 
so_lambda: λ2x.t[x]
, 
subtype_rel: A ⊆r B
, 
nat: ℕ
, 
int_seg: {i..j-}
, 
lelt: i ≤ j < k
, 
le: A ≤ B
, 
so_apply: x[s]
, 
uimplies: b supposing a
, 
all: ∀x:A. B[x]
Lemmas referenced : 
not_wf, 
assert_wf, 
isvarterm_wf, 
equal-wf-base, 
all_wf, 
int_seg_wf, 
set_subtype_base, 
le_wf, 
int_subtype_base, 
length_wf, 
bound-term_wf, 
term-bts_wf, 
term_wf, 
list_wf, 
nat_wf, 
istype-nat, 
istype-universe
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation_alt, 
introduction, 
cut, 
sqequalRule, 
functionEquality, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
hypothesis, 
productEquality, 
because_Cache, 
closedConclusion, 
natural_numberEquality, 
equalityTransitivity, 
equalitySymmetry, 
lambdaEquality_alt, 
applyEquality, 
setElimination, 
rename, 
productElimination, 
inhabitedIsType, 
independent_isectElimination, 
universeIsType, 
axiomEquality, 
isect_memberEquality_alt, 
isectIsTypeImplies, 
functionIsType, 
instantiate, 
universeEquality
Latex:
\mforall{}[opr:Type].  \mforall{}[sort:term(opr)  {}\mrightarrow{}  \mBbbN{}].  \mforall{}[arity:opr  {}\mrightarrow{}  ((\mBbbN{}  \mtimes{}  \mBbbN{})  List)].  \mforall{}[t:term(opr)].
    (correct-sort-arity(sort;arity;t)  \mmember{}  \mBbbP{})
Date html generated:
2020_05_19-PM-09_58_10
Last ObjectModification:
2020_03_11-PM-03_54_25
Theory : terms
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